Fabric of church beam a male bishop installed (8)
I believe the answer is:
chambray
'fabric' is the definition.
(chambray is a kind of fabric)
'church beam a male bishop installed' is the wordplay.
'church' becomes 'ch' (common abbreviation).
'beam' becomes 'ray' (synonyms).
'male' becomes 'm' (common abbreviation).
'bishop' becomes 'B' (abbreviation used in chess).
'installed' means one lot of letters goes inside another.
'a'+'m'+'b'='amb'
'ch'+'ray'='chray'
'chray' placed around 'amb' is 'CHAMBRAY'.
'of' acts as a link.
(Another definition for chambray that I've seen is " Mary Bach makes a lightweight woven fabric".)